A new optimizer is presented for the extraction of the small-signal equivalent circuit elements (X) of a GaAs FET from its measured scattering (S) parameters. The approach is a combination of the damped Gauss-Newton method, for the least-squares fitting of the S parameters, and the random search generalized simulated annealing (GSA). Novel features of the proposed approach include (i) an improved Kondoh step-by-step optimization of the objective functions grouped according to their sensitivity to variation of key equivalent circuit parameters (X), and (ii) exploitation of the advantages derived from a transformation of the objective functions from scattering parameters to impedance parameters.